The draw keeps the race for Champions League qualification wide open.
Fellaini might have been about to receive a second booking anyway for fouling Aguero when he went head to head with City's striker and aimed a butt in the 83rd minute, earning a straight red card.
City sent on fit-again striker Gabriel Jesus in an attempt to score a late goal and the striker had a stoppage-time headed goal disallowed for offside in a tense finish at Etihad Stadium.
City captain Vincent Kompany refused to criticise his Belgium team-mate Fellaini, despite being on the opposing side at the Etihad.
"I don't get involved," the defender said. "He's my teammate ultimately and whether he's red or blue I support him in every way. I don't want to get involved."
Kompany did, however, praise United's strike force and highlighted the pace of Marcus Rashford and Anthony Martial particularly.
"They are lightening quick and with a bit more experience they are going to cause a lot more trouble," Kompany added.
But United manager Jose Mourinho's defensive tactics suffocated another heavyweight rival - it resembled an attack vs defence exercise in the second half - but whether a goalless draw does the team any good is open to question.
It left Mourinho's team in fifth place, both a place and a point behind City with five games remaining in the race for a top-four finish to qualify for the Champions League. Liverpool are a point ahead of City and have played a game more than both Manchester clubs.
United have the more difficult run-in, with trips to come to Tottenham and Arsenal, and are still involved in the Europa League.
By becoming only the second team to stop City from scoring at home this season, United extended their unbeaten run in the league to 24 games dating to a loss at Chelsea in October.